AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62⁰, then find the measure of the minor arc AC.

If x + y + 3 = 0 , then find the value of x³+y³-9xy+9.

A sold a mobile phone to B at a gain of 25% and B sold it to C at a loss of 10%. If C paid ₹5,625 for it, how much did A pay (in ₹) for the phone?

If 4sin²θ=3(1+cosθ),0⁰<θ<90⁰, then what is the value of (2tanθ+4sinθ-secθ)?

A pole 23 m long reaches a window which is 3 m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4 is m high. What is the width (in m) of the street? 

Select the odd group of numbers. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g.13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

If A × B means that A is the brother of B, A – B means that A is the sister of B, A + B means that A is the father of B then which of the following expression shows that P is the paternal aunt of R?

A # B means ‘A is the sister of B’
 A @ B means ‘A is the daughter of B’
 A & B means ‘A is the husband of B’
 A % B means ‘A is the father of B’
 If A % B & C # D @ E, then how is B related to E?